When you discount future flows, the maximum sustainable yield is larger than the maximum flow of profits. off the top of my head, I think the slope at the "optimum" will be reduced in direct proportion to the interest/discount rate.

So instead of harvesting 100 units annually from a population of 1000 for eternity, my impatience together with indifference for the future may lead me to prefer to act as though there is a specific discount/interest rate by harvesting 110 units this year, 105 the following year, and accept a long-term equilibrium harvest of 98 units per year at a population of 970, for example. Consider this as normalized population per square km since a total population of 970 is basically almost extinct.

So, in this situation, a person can "rationally" deplete a resource to below the MSY. If the interest/discount rate is 10%, they could easily prefer to deplete a resource over 10-20 years rather than seeking a maximum sustainable yield. This is one of many reasons that improving credit market conditions in many areas can contribute to more sustainable practices, especially if those who exploit natural resources are encouraged to make the calculus more carefully, in particular in cases where there is not an existing tradition/ethic of sustainability/conservation.

A good book for this sort of stuff is "Optimal Control Theory and Static Optimization in Economics" by Leonard and Van Long. There are good exercises designed to be done in Excel, and if you don't get tied up in knots with deep knowledge of every mathematical detail, you should have a good understanding of how to present and develop various models for these contexts by just going through the motions of highlighting what you're not sure about and proceeding step by step through the exercises.

Yes, I will have a look on the book you mentioned. Here I want to raise another question about viability of the discount  rate method in a multi-species tropical fishery. (This is one of the demerits in the MSY method too as MSY is calculated for each species separately.) While fishing in a muliti-species fishery this is practically very tedious to distinguish between the threatened species for which the harvest rate should be kept at a much lower level.

Again comes the age distribution of the population of a particular species. For a population of which a large portion is juvenile, the harvest rate should be low. But for a relatively older population for whom the breeding period is over we can keep the harvest rate at a desired level. I see no feasible approach to deal with these intra-species and inter-species differential harvest rates.

Is this a theoretical work or will you need to estimate specific parameters for a specific context (this could take years of periodic data collection to get anything remotely accurate, but perhaps a local fishery service can start you off with some background historical data)?

I think if you could make a succinct demonstration of a theoretical methodology which COULD be practically applied to analysis of multispecies situation where one species is targeted for conservation efforts in a fishery where there is a relevant level of cross-catching, etc., then you would already have done a lot.

In my opinion, hyperbolic discounting is a more accurate reflection of how real people actually evaluate these sorts of things over timeframes which exceed 5, 10 or 20 years, but most often it's not worth the distraction this can make from the main point of interest, and you can just comment that the outcomes would be more/less over various timeframes under hyperbolic discounting. In which case you may as well just use the standard discounting approach, but it is well worth wading through some literature on alternatives if you have thoughts to do empirical work on it at some stage as well.

@Nathan Weatherdon, I want to do a study on sustainability of the current management system of the tropical fisheries of Assam for which, I am in search of a suitable scale of sustainability (which is practically feasible to apply) to gauge the situation.

Unless you have very good reasons to believe otherwise, I  would treat the data with at least a goods few grains of salt for Assam. My understanding is that various governance structures are quite carefully thought through for certain reasons, but I sort of doubt that this transmits to a particularly high current prioritization of good data on fisheries.

I would think that data collection methods would differ a lot for these mountain river fish (which I assume you speak of) and fish in lakes or farmed ponds. For example, its less realistic to work with the idea that you can drop a million fry in somewhere and be able to reliably know what effect this had on fish populations throughout a river system, i.e., hard to know if/how much it's worth it if a population is depleted or can profitably received alternative inputs.

The experimental design for population estimation isn't my strength. I know you need samples at different stages of the population cycle and will need to have a well-defined trapping/catching process. Could the concern be that certain species have combined population dynamics and catch rates with existing technologies in the area which warrant intervention in the form of discouraging catching these specific species, or is this a question of demonstrating an economic valuation of a conservation effort? The only river fish population I know much about is salmon, but I imagine there must be an awful lot of economic analysis of Chinese river fish populations, although a) they probably have not been translated into English and b) they may not even be easily available in any language. Are there similar population to, say, rivers in highland areas of Sichuan? ...  just as a thought on who might have some existing research that's more closely related to fisheries in Assam.

As a short answer, and short for your point too I would think that you could show MSY and compare to sustainable yields in a low-interest rate and high-interest rate situation. But I really think it will be very difficult to get reliable estimation of the relevant parameters in these lake ecosystems.

Viability theory provides a new(-sh) framework for modelling and solving sustainability problems. Have a look at  http://link.springer.com/article/10.1007/s10287-013-0189-z  and the links there provided.

Sorry, it was "Resource Economics" by JM Conrad with the Excel modelling exercises. But the other book is very useful too for this kind of stuff. Best of luck!

thank you all very much for your suggestions!

Once again, I suggest you drop optimisation and use viability theory. It is more general and more real-life. Use the above link to begin with. 

See the attached link to  "The efficacy of fisheries management strategies: A case study of the Gulf of Maine Redfish fishery" for some insights on maximum sustainable yield and fisheries management from a different perspective. 

Chapter The efficacy of fisheries management strategies: A case stud...

This is rather my opinion, than an answer to your question. I give it anyway: I would not suggest using MSY at all, since the simplifcations in the underlying model are just too severe. E.g. the model usually ignores species interactions, environmental oscillations, bycatch, age and size distributions, difficulties in obtaining the necessary data on populations size and growth rates, etc. Estimation of potential and sustainable catch should be based on multi-species models and should consider ecosystem services beyond food provisioning.

I would look at the inputs to the logic.  Discount rates, technical change, relative prices and externalities are all important.  I co-authored a number of papers concerning Preservation of the Hell's Canyon with John Krutilla and Anthony Fisher. I would start there. 

I was just reading your question and can give you some insight into the struggles we have in Europe to use MSY as a management target. The problem is, as many others already mentioned, that we work in a multi-species environment. In Europe the advisory committee I am part of (Scientific, Technical and Economic Committee for Fisheries of the European Commission (STECF)) is arguing that we need to choose the fishing mortality which gives us the possibility to have a stock biomass at MSY level as the management target. This means that you are not going for a specific biomass level but regulate the fishing effort in a way that allows the stock to grow to MSY (if it is below, of course). However, this is normally not how people interpret the MSY principle (stock biomass that allows us to fish at MSY). Nevertheless, this basically means that we regulate what we can influence: the fishing effort. In a multi-species environment not every stock will be at MSY at the same time and with the fishing mortality at MSY level we can live with fluctuating stock levels without compromising the overall MSY objectives (if we accept that as the objective). 

The problem with this is that you need good data on stocks to really be able to calculate stock biomass or fishing mortality rates. In cases were you don't have such data, which is the case also for many stocks in European Waters, we work with proxies. As I am not a fisheries biologists I am not that familiar with these proxies but you can look on the website of STECF (http://stecf.jrc.ec.europa.eu/reports/review-advice) or ICES (www.ices.dk) to search how the biologists work with data poor stocks.

All this is about biology and not about economics. Usually we discuss Maximum Economic Yield as the primary objective (here is an article which others may already suggested: https://crawford.anu.edu.au/pdf/staff/quentin_grafton/2010/AJARE_BMEY_2010.pdf).

However, this is basically a theoretical concept. What we try to analyze at the moment is the possibility how to translate that into a workable objective. For that we discuss Gross Value Added (GVA) or Profit Maximization as possible Proxies. An idea could be also to try to have a 'earned interest on capital' as a proxy, where we e.g. go for a 5% interest rate as objective. The problem is that it may hard to get all of this information for many fisheries. We have the advantage that we have a regularly economic data collection to have at least some basic data for it.

I don't think that this really answers your question but probably a bit food for thought.

https://ec.europa.eu/fisheries/sites/fisheries/files/docs/body/msy_en.pdf

http://www.pewtrusts.org/~/media/assets/2015/03/turning_the_tide_msy_explained.pdf

http://unepscs.org/Refugia_Training/Fisheries%20Management%20Principles%20and%20Concepts/03-Concept-Maximum-Sustainable-Yield-Fisheries-Asia.pdf